Many years ago, when I was a drama student at the Central School of Speech and Drama, I took part in a read-through of Chekhov's The Three Sisters. I played Masha; I found her annoying, selfish, self-indulgent - and magnificent. I didn't know much about Chekhov, but I also found the play hilarious. I was the only one who did: everyone else had their serious "Chekhov face" on.

A year later, I spent a term at the Moscow Arts Theatre School, studying Chekhov under men old enough to have studied under Stanislavski himself. At the Moscow Arts Theatre, I watched a production of Chekhov's The Seagull. The audience was an eclectic mix: Russian babushkas, swaddled and looking like my great-grandmother, who hailed from Kiev; intellectuals in black rollnecks; glamorous women shedding fur hats to reveal high cheekbones. Again, I found the production moving but hilarious. I couldn't understand a word, but I was laughing and crying almost in the same breath - and so were the audience. This time I wasn't alone. In the country of his birth, I found I had hit on something all those months earlier: Chekhov's plays have funny bones.

Chekhov wrote about a world I recognised from my childhood - where intense pain is covered by bravura and humour, and where intense longing is masked by self-deprecation and wit. There was the same obsession with death, the same fierce familial loyalty, the same tendency toward melodrama - as well as a great passion for food.

Re-reading The Three Sisters, I saw that the Prozorov family were clearly Jewish. The pieces of a jigsaw began to form in my mind. Was it possible to take this Chekhovian scenario and turn the story of a family stuck out in the sticks and pining for a Moscow that probably never existed, into a warm, witty Jewish adaptation, by way of Woody Allen? Is it possible to take a family who have the Holocaust hanging over them, and still have them laugh and moan and bicker while wondering what's for breakfast?

Woody Allen once said that "food is funny", and I know what he means. My family, from my 88-year-old Russian great-grandmother right down to my baby cousin Ben, plus out-of-towner guests, could sit at a Friday night dinner table for a three-hour meal while debating famine, war, plague, politics, the poll tax, student loans, the National Health Service, racism, the Holocaust and the royals with passion and tears, raised voices, a storming out, vows never to speak again, divorces cited - and still have everyone back at the table with the mention of a cup of coffee and a slice of almond cake.

I love Woody Allen's work, and he openly acknowledges his own debt to Chekhov: most obviously in Hannah and Her Sisters and Bullets Over Broadway. "I'm crazy about Chekhov," he once told a journalist. "I never knew anybody that wasn't! People may not like Tolstoy. There are some people I know that don't like Dostoyevsky, don't like Proust or Kafka or Joyce or TS Eliot. But I've never met anybody that didn't adore Chekhov." I think he's right. Chekhov is loved because he loved people - he knew and understood them, warts and all. A doctor, he said that he first had to make his patients laugh and only then could he treat them. More than anyone, Chekhov and Woody Allen understand that humour is a highly sophisticated defence mechanism (check out the similarities between Zelig and Dr Chebutykin in Three Sisters).

When I started work on what would eventually become Three Sisters on Hope Street, I was reminded of the night my father died of a sudden heart attack in my arms. I sat huddled on the bed with my younger sister, shell-shocked, and for no reason we started laughing and couldn't stop. It was 5am: we'd been crying hysterically for hours, and then at the mention of my father's chronic hypochondria and how he'd apparently been right all along, we just sat and laughed and laughed. And then cried.

Chekhov knew that he was writing comedy. He stormed out of an early reading of The Three Sisters, horrified when the cast and director wept from act two to the end. I took inspiration from this and also from Woody Allen's ability to create dark but very funny versions of Chekhov's originals. In my version of the play, the doctor became a self-hating back-street abortionist with a penchant for a flutter and a drink, but also with a song in his heart. Anfisa, the old maid, is my great-grandma, who fled the pogroms at 16 but was never really at home in England; at times she felt like the "domestic" rather than a fully fledged member of the family. The three sisters and their brother are all child-adults, emotionally arrested since the death of their mother.

Two years ago, after an intense 18 months playing Chrissy Watts on EastEnders - and 15 years after I first started work on the play - I returned to the project. A chance conversation in the back of a taxi led me to collaborate with Diane Samuels, who loved the idea and offered up Liverpool, her hometown, as the perfect setting. We agreed on the dates 1945-48 - that pregnant pause after the second world war when the world began to rebuild itself. Liverpudlians have their own black sense of humour and comic timing, born out of having their city blown to smithereens during the war. Diane and I laughed a lot as we created Debbie Pollack, Dr Nate Weinberg, Mordy and our cast "of thousands". I'd like to think that Chekhov and Woody Allen would approve.

· Three Sisters on Hope Street is at the Everyman, Liverpool, until February 16. Box office: 0151-709 4776. Then at the Hampstead, London

· This article was amended on Saturday February 9 2008. The standfirst to this article, and the caption to a photograph that accompanied it in the print edition, should have made clear that Three Sisters on Hope Street is by Diane Samuels and Tracy-Ann Oberman. They referred only to Oberman. This has been corrected.